# Math

From a point x = 110 feet in front of a public library, the angles of elevation to the base of the flagpole and the top of the flagpole are θ = 27.5° and 39° 45', respectively. The flagpole is mounted on the front of the library's roof. Find the height of the flagpole.

STEP 1: Let F be the height of the flagpole and L be the height of the public library. Convert the angle 39° 45' into decimal form.
Use this value and an appropriate trigonometric function to find F + L, the total height of the library and flagpole.
F + L=

STEP 2: Find the height of the library, L.

STEP 3: Subtract your result from Step 2 from your latter result in Step 1 to determine the height of the flagpole, F.

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tan (39 + 45/60) = (F+L)/110 find F+L
tan (27.5) = L/110 find L
so subtract

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2. 39° 45' = ( 39 + 45 / 60 )° = 39.75°

tan 39.75° = ( F + L ) / 110

F + L = 110 ∙ tan 39.75°

F + L = 110 ∙0.831691221 = 91.48603431 ft

height of the library:

tan 27.5° = L / 110

L = 110 ∙ tan 27.5° = 110 ∙ 0.520567051 = 57.26237561 ft

height of the flag:

F = F + L - L = 91.48603431 - 57.26237561 = 34.2236587 ft

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